A pumpkin patch contains x pumpkins that weigh 10 pounds each and y pumpkins that weigh r pounds each. If the average (arithmetic mean) weight of the pumpkins is 12 pounds, what is the value of r?(1) There are five more heavier pumpkins than lighter pumpkins.(2) The weight in pounds of each of the heavier pumpkins is 3 more than their number.

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.D. Either statement BY ITSELF is sufficient to answer the question.E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(C) The original statement says the average weight of a pumpkin is 12 pounds. Since x pumpkins weigh 10 pounds each, the y pumpkins must be heavier.Writing an equation for the average weight of the pumpkins is (10x + ry) / (x + y) = 12. This equation has three unknowns.Solve for r to get:r = 12 + (2x/y)

Statement (1) defines the relationship between x and y as y = x + 5 or y = x – 5. Plug in the formula for r to getr = 12 + (2(y – 5)/y)r = 14 – 10/yPlug in couple values of y (greater than 5) to see that they yield different results for r.Statement (1) is not sufficient.

Statement (2) gives the relationship between y and r as r = y + 3. This isn't enough information as you can plug it into the original equation and see that too many variables remain. Plug in couple values for y to see that we get different possible valuee of r and x.

Using the given with the equations from (1) and (2), the system is(10x + ry) / (x + y) = 12y = x + 5r = y + 3

"...Since x pumpkins weigh 10 pounds each, the y pumpkins must be heavier..." is not an objective step. Please explain how you decide y to be heavier and not x.

We should consider this sentence together with the previous one:

Quote:

The original statement says the average weight of a pumpkin is 12 pounds. Since x pumpkins weigh 10 pounds each, the y pumpkins must be heavier.

If the y pumpkins weighed less than 12, then the average weight of all the pumpkins would be less than 12 as well, because all the pumpkins would simply weigh less than 12.So the y pumpkins weigh more than 12 and therefore more than 10, which means that they are heavier than the x pumpkins.

Is it required to solve the entire question? What do we have to do: just to form the equations or just to find out how many unknow variables the equations have? From this information, can we comment as to whether we can get the answer or not?

On the other hand, if you do NOT need to find ALL the variables, but just one, two equations might be enough, e.g.:x + y + z = 1x + y = 0So z = 1.

Therefore you should NOT just calculate the number of equations and variables you have, BUT to analyze:- are these linear equations?- what variable(s) do you need to solve for?- are any of the equations proportional?

So you do NOT need to do all the calculations, but to be sure that calculations will give you the answer.

This question does not tell us which type of pumpkin is the heavier one. In that case how can we take the validtity of the statement that x = y + 5. It could be possible that the pumpkin with 10 pouns is heavier one.

We know that r > 12, otherwise the average of the pumpkins would not be 12. So the left term is positive. Hence the right term needs to be positive as well: x is a positive quantity => 14 - r > 0. So the only possibility for is to be 13! Solved only with equation 1!

Who is online

Users browsing this forum: No registered users and 3 guests

You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum